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Finite Element Analysis for Machine Design

This course introduces classical and modern techniques for the analysis and design of electromagnetic devices such as electric machines and transformers. Emphasis is placed on finite element analysis (FEA), winding analysis, and magnetic material modeling. Students apply electromagnetic theory to practical design problems using commercial simulation software.

Instructor
Objectives
  • Classify electromagnetic partial differential equations and apply appropriate boundary conditions.
  • Apply electromagnetic field theory concepts including magnetostatics, quasi-statics, and magnetic scalar potential.
  • Formulate electromagnetic problems using variational methods and weighted-residual approaches.
  • Implement the finite element method, including shape functions and step-by-step solution procedures.
  • Model permanent magnet materials and represent them using equivalent magnetic circuit models.
  • Analyze electrical windings using turns functions, winding functions, and distributed winding theory.
  • Evaluate winding factors, fractional-slot and concentrated winding configurations, and slotting effects.
  • Apply Carter’s coefficient and star-of-slot analysis in electric machine design.
  • Solve practical electromagnetic design problems using commercial finite element analysis software.
  • Analyze and design transformers and permanent magnet machines under voltage and current constraints.
Textbooks

Electromagnetic Modeling by Finite Element Methods

J. P. A. Bastos, N. Sadowski · Marcel Dekker (CRC Press)

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Electrical Machine Analysis Using Finite Elements

N. Bianchi · CRC Press

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Variable Speed Generators

I. Boldea · CRC Press

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Permanent Magnet Motor Technology: Design and Applications

J. F. Gieras · CRC Press

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Permanent Magnet Synchronous and Brushless DC Motor Drives

R. Krishnan · CRC Press

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Introduction to AC Machine Design

T. A. Lipo · University of Wisconsin Publication (Wiley)

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Finite Element Analysis of Electrical Machines

S. Salon · Springer

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Numerical Techniques in Electromagnetics

M. N. O. Sadiku · CRC Press

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Modules
1 Module 01: Introduction to FEA for Machine Design (Part 1)

Description: Introduction to Finite Element Analysis (FEA) for electric machines, covering the scope of the course and the role of numerical methods in electromagnetic design.

2 Module 01: Introduction to FEA (Part 2)

Description: Continuation of the introduction, setting up the mathematical framework for solving electromagnetic problems using FEA.

3 Module 02: Maxwell's Equations & Boundary Conditions (Part 1)

Description: Review of Maxwell's equations as they apply to low-frequency magnetic problems and the definition of boundary conditions.

4 Module 02: Maxwell's Equations & Boundary Conditions (Part 2)

Description: Deep dive into differential equations used in FEA, specifically focusing on the magnetic vector potential formulation.

5 Module 03: Finite Element Discretization (Part 1)

Description: Fundamentals of meshing and discretizing the domain into finite elements to solve partial differential equations.

6 Module 03: Finite Element Discretization (Part 2)

Description: Advanced meshing techniques and the impact of mesh quality on solution accuracy and convergence.

7 Module 04: Magnetostatics & Linear Materials (Part 1)

Description: Solving magnetostatic problems where material properties are linear, focusing on air gaps and core materials.

8 Module 04: Magnetostatics & Linear Materials (Part 2)

Description: Practical examples of linear magnetostatic simulations and analysis of flux density distribution.

9 Module 05: Nonlinear Materials & Saturation (Part 1)

Description: Introduction to nonlinear magnetic materials, B-H curves, and modeling magnetic saturation in electrical steels.

10 Module 05: Nonlinear Materials & Saturation (Part 2)

Description: Newton-Raphson methods and iterative solvers for handling nonlinear material properties in FEA.

11 Module 06: Permanent Magnet Modeling (Part 1)

Description: Techniques for modeling permanent magnets (PM) in FEA, including remanence and coercivity definitions.

12 Module 06: Permanent Magnet Modeling (Part 2)

Description: Simulation of PM machines, setting magnetization direction, and analyzing the operating point of magnets.

13 Module 07: Eddy Currents & Time-Harmonic Analysis (Part 1)

Description: Introduction to eddy currents, skin effect, and time-harmonic (AC) solvers for steady-state analysis.

14 Module 07: Eddy Currents & Time-Harmonic Analysis (Part 2)

Description: Loss calculation in conductors and laminations using AC magnetic simulation.

15 Module 08: Transient Magnetic Analysis (Part 1)

Description: Setup for transient solvers to analyze time-stepping phenomena, motion, and dynamic performance.

16 Module 08: Transient Magnetic Analysis (Part 2)

Description: Coupling motion with magnetic fields to simulate rotating machines and torque production over time.

17 Module 09: Force & Torque Calculation Methods (Part 1)

Description: Methods for calculating electromagnetic forces and torque, including the Maxwell Stress Tensor and Virtual Work method.

18 Module 09: Force & Torque Calculation Methods (Part 2)

Description: Analyzing torque ripple, cogging torque, and optimizing geometry to minimize vibrations.

19 Module 10: Winding Layout & Circuit Excitation (Part 1)

Description: Defining coil terminals, winding phases, and linking external circuits to the FEA model.

20 Module 10: Winding Layout & Circuit Excitation (Part 2)

Description: Advanced circuit coupling, including diode rectifiers and inverter switching effects in FEA.

21 Module 11: Core Loss Calculation (Part 1)

Description: Theoretical background of core losses (hysteresis, eddy, excess) and the Bertotti model.

22 Module 11: Core Loss Calculation (Part 2)

Description: Applying core loss coefficients in FEA software and interpreting loss density maps.

23 Module 12: Thermal Analysis Coupling (Part 1)

Description: Introduction to Multiphysics: coupling electromagnetic losses to thermal solvers.

24 Module 12: Thermal Analysis Coupling (Part 2)

Description: Setting up thermal boundary conditions and steady-state thermal simulations for motors.

25 Module 13: Advanced Machine Simulation (Part 1)

Description: Advanced topics in machine simulation, potentially covering 3D effects or specific machine topologies.

26 Module 13: Advanced Machine Simulation (Part 2)

Description: Case studies and problem-solving sessions using commercial FEA software.

27 Module 14: Special Topics in FEA (Part 1)

Description: Focused analysis on specific design challenges, such as demagnetization analysis or fault conditions.

28 Module 14: Special Topics in FEA (Part 2)

Description: Continuation of special topics, analyzing harmonics and parasitic effects.

29 Module 15: Design Optimization Strategies (Part 1)

Description: Strategies for using FEA in an iterative design loop to optimize motor performance.

30 Module 16: Practical FEA Lab Session (Part 1)

Description: Hands-on demonstration or walkthrough of a complete machine design project.

31 Module 16: Practical FEA Lab Session (Part 2)

Description: Finalizing the design project, post-processing results, and generating reports.

32 Module 17: Course Conclusion & Future Trends (Part 1)

Description: Summary of the course concepts and a look at future trends in electromagnetic simulation.

33 Module 17: Course Conclusion & Future Trends (Part 2)

Description: Closing remarks and final Q&A on FEA applications in industry.

Assignments

Assignment 1 - PDE Classification & Numerical Methods (Ritz & Weighted-Residual)

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Assignment 2 - FEA Theory & Magnetic Circuit Simulation

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Assignment 3 - Permanent Magnet Sizing & Time-Varying Flux Analysis

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Assignment 4 - Stator Winding Design & Fourier Analysis

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Project 1 - Development of a 2D Finite Element Solver

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Project 2 - Fractional Slot Winding Design & JMAG Simulation

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